Question

select the correct answer.

which of the following trinomials could represent the product \\((x + m)(x + n)\\) if \\(m = 5\\) and \\(n = -7\\)?

• \\(x^2 - 2x - 35\\)
• \\(x^2 + 2x - 35\\)
• \\(x^2 + 35x + 2\\)
• \\(x^2 - 12x - 35\\)

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Substitute the values of \( m \) and \( n \)

Substitute \( m = 5 \) and \( n = -7 \) into the expression \( (x + m)(x + n) \):

$$ (x + 5)(x - 7) $$

Step 2: Expand the expression

Multiply the binomials using the FOIL method (First, Outer, Inner, Last):

$$ (x + 5)(x - 7) = x^2 - 7x + 5x - 35 $$

Step 3: Combine like terms

Combine the \( x \) terms:

$$ x^2 - 2x - 35 $$

Answer:

\( x^2 - 2x - 35 \) (the first option)